Numerical solution for the fluid flow between active elastic walls

Fatima Ahmed, Dmitry Strunin, Mayada Mohammed


We analyse a model of the fluid flow between elastic walls simulating arteries actively interacting with the blood. The lubrication theory for the flow is coupled with the pressure and shear stress from the walls. The resulting nonlinear partial differential equation describes the displacement of the walls as a function of the distance along the flow and time. The equation is solved numerically using the one-dimensional integrated radial basis function network method. A solution in the form of a self-sustained train of pulses is obtained. Numerical experiments demonstrate the process of formation of the train from randomly chosen initial conditions. Dependence of the pulses on the boundary conditions is explored.

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